In view of the fact this thread has been complicated enough already I don't really want to throw any more into the mix BUT the 1901 'Kate' with John and Margt. J. Cavanagh as reported by venelow is not Catherine Bridget and felt I had to mention that.
It's somewhat bizarre as I've looked at the census' before and after 1901, studied subsequent BMD's and the scenario is this: in Dec.1882 Durham an Anthony Joyce married a Margaret Jane Grace (in 1891 family listed as Joice) - Mary b.1883 Thornley (birth Sept.1883 Easington) and the remaining 5 in Gateshead - Thomas Sept.1885, Hannah Sept.1887, Anthony Mar.1890, Margaret June 1893 and Catherine Sept.1894 (the latter being the 1901 'Kate'). Anthony Joyce senior died Newcastle upon Tyne in 1895 and by 1901 Margaret Jane and her children are with John Cavanagh (who may or may not be the one mentioned earlier in the thread) and they are all listed as Cavanagh (cannot find Anthony born 1890 but he appears later). There is no marriage between Margaret Jane and John although the 1 year old in 1901 is clearly a child of John Cavanagh. The following census lists the whole family as 'Joyce', including John himself who signed as such (see what I mean about bizarre). His child with Margaret Jane is shown as son, but 3 of her earlier children shown as 'Boarders'.
You can no doubt see why I didn't want to elaborate on this but needed to prove as best I can why 'Kate' Cavanagh wasn't Catherine Bridget Kavanagh, never believing it would turn into such a saga. At the moment we are back to square one in that Margaret E (for Elizabeth) and Catherine Bridget are still missing on 1901 census although I am thinking they should probably be in Newcastle upon Tyne as that is where son John Thomas died in 1900 and where Margaret married Patrick McIntyre in 1902.
So, eysham, after you've read the last 2 posts put them out of your mind as we are only concentrating on Thomas now in an effort to unravel that particular tangle (we sure don't need another one).
Annette